All Molecular Surfaces are Equal: Demanding Invariance of Predictions in Linear Single-Variable Models

Author
Kjønstad, Eirik
Moxnes, John Fredrik
Jensen, Tomas Lunde
Unneberg, Erik
Date Issued
2016
Keywords
Elektrontetthet
Elektrostatisk potensial
Lineær modellering
Molekylær overflate
DOI
10.1080/00268976.2016.1140842
Collection
Articles
Description
Kjønstad, Eirik; Moxnes, John Fredrik; Jensen, Tomas Lunde; Unneberg, Erik. All Molecular Surfaces are Equal: Demanding Invariance of Predictions in Linear Single-Variable Models. Molecular Physics 2016 ;Volum 114.(10) s. 1559-1567
1314878.pdf
Size: 829k
Abstract
The molecular surface has been suggested to be a region of the molecule where information of non-covalent intermolecular interactions is present. Many workers have pursued this idea by constructing models based on statistical parameters Φ extracted from the electrostatic potential on a particular molecular surface. We claim that a better approach is to define a family of equivalent molecular surfaces, each associated with a particular electron density ε. The demand that any model must give the same predictions on all such molecular surfaces yields a mathematical requirement restricting the space of permissible parameters. We prove that linear single-variable models of the form property = αΦ + β will only yield invariant predictions if the parameter values of Φ computed on equivalent surfaces are linearly related. This claim is not restricted to the use of the electrostatic potential, but holds for any parameter extracted from the surface of molecules. By using a set of 44 molecules we also demonstrate that a frequently used aspect of the electrostatic potential, that of ‘imbalance’ of negative and positive values, fails to satisfy the linearity requirement. It is argued that multi-variable models should only include parameters that satisfy the single-variable requirement.
View Meta Data